. For a symmetric matrix M E RnAn we denote respectively )min (M) and max(M) the smallest and largest eigenvalue of M. Let f : R" - R be a function that is twice continuously differentiable. We assume that y def inf Amin (Hf (x) ) CERn and def sup Amax (Hf(x) ) TERn are both finite. Show that for all x, h E Rn: f ( x) + ( Vf ( xx), h) + = 1/h/12